14 is carréphylic - approach of √14 ~ 3.7416573868
Subsequent approximations of √14 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-14p2 = 1 | | | |
| d = distance to nearest square N2: | -2 | | | |
| Smallest non-trivial s: | (2*16-2)/2 | rational: 30 | actual: 30 | ⇒ F=60 |
| Smallest non-trivial p: | 2*4/2 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value tq-blocks: | 42-14*12: | +2 | | |
| v-value qt-blocks: | 72-14*22: | -7 | | |
| Number of series: | 8 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 15 | 449 | 13455 | 403201 | 12082575 | ... |
| p | 0 | 4 | 120 | 3596 | 107760 | 3229204 | ... |
| In the numerator: | U(1,15)30 | = | 1/2*U(2,30)30 | - | half the secundus of 30. |
| In the denominator: | U(0,4)30 | = | 4*U(0,1)30 | - | the 4-fold primus of 30. |
| as well as ... |
| In the numerator: | U(0,56)30 | = | 56*U(0,1)30 | - | the 14*4-fold primus of 30. |
| In the denominator: | U(1,15)30 | = | 1/2*U(2,30)30 | - | half the secundus of 30. |
| and ... |
| In the numerator: | U(4,4)30 | = | 4*U(1,1)30 | - | the 4-fold tertius of 30. |
| In the denominator: | U(-1,1)30 | = | | - | the quartus of 30. |
| and ... |
| In the numerator: | U(-7,7)30 | = | 7*U(-1,1)30 | - | the 7-fold quartus of 30. |
| In the denominator: | U(2,2)30 | = | 2*U(1,1)30 | - | the 2-fold tertius of 30. |
